Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.961 |
Dual form | 1216.2.i.f.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | + | 3.46410i | −0.894427 | + | 1.54919i | −0.0599153 | + | 0.998203i | \(0.519083\pi\) |
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.73205i | 0.277350 | + | 0.480384i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | + | 3.46410i | 0.516398 | + | 0.894427i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | − | 4.33013i | −0.114708 | − | 0.993399i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | − | 9.52628i | −1.10000 | − | 1.90526i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | − | 3.46410i | −0.371391 | − | 0.643268i | 0.618389 | − | 0.785872i | \(-0.287786\pi\) |
−0.989780 | + | 0.142605i | \(0.954452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0000 | −1.79605 | −0.898027 | − | 0.439941i | \(-0.854999\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | + | 2.59808i | −0.261116 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.50000 | + | 7.79423i | −0.702782 | + | 1.21725i | 0.264704 | + | 0.964330i | \(0.414726\pi\) |
−0.967486 | + | 0.252924i | \(0.918608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | + | 3.46410i | −0.304997 | + | 0.528271i | −0.977261 | − | 0.212041i | \(-0.931989\pi\) |
0.672264 | + | 0.740312i | \(0.265322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.00000 | −1.19257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | + | 10.3923i | 0.875190 | + | 1.51587i | 0.856560 | + | 0.516047i | \(0.172597\pi\) |
0.0186297 | + | 0.999826i | \(0.494070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | + | 1.73205i | 0.140028 | + | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | − | 1.73205i | −0.137361 | − | 0.237915i | 0.789136 | − | 0.614218i | \(-0.210529\pi\) |
−0.926497 | + | 0.376303i | \(0.877195\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | − | 10.3923i | 0.809040 | − | 1.40130i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | − | 1.73205i | −0.529813 | − | 0.229416i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.500000 | + | 0.866025i | −0.0650945 | + | 0.112747i | −0.896736 | − | 0.442566i | \(-0.854068\pi\) |
0.831641 | + | 0.555313i | \(0.187402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.00000 | −0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.50000 | + | 7.79423i | 0.549762 | + | 0.952217i | 0.998290 | + | 0.0584478i | \(0.0186151\pi\) |
−0.448528 | + | 0.893769i | \(0.648052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50000 | − | 7.79423i | 0.526685 | − | 0.912245i | −0.472831 | − | 0.881153i | \(-0.656768\pi\) |
0.999517 | − | 0.0310925i | \(-0.00989865\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.0000 | −1.27017 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.00000 | 0.548821 | 0.274411 | − | 0.961613i | \(-0.411517\pi\) | ||||
0.274411 | + | 0.961613i | \(0.411517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 6.92820i | −0.433861 | − | 0.751469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.00000 | −0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | + | 15.5885i | 0.953998 | + | 1.65237i | 0.736644 | + | 0.676280i | \(0.236409\pi\) |
0.217354 | + | 0.976093i | \(0.430258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.00000 | + | 8.66025i | −0.518476 | + | 0.898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.0000 | + | 6.92820i | 1.64157 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | + | 0.866025i | −0.0507673 | + | 0.0879316i | −0.890292 | − | 0.455389i | \(-0.849500\pi\) |
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | − | 5.19615i | −0.301511 | − | 0.522233i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 10.3923i | 0.597022 | + | 1.03407i | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.0000 | −1.54678 | −0.773389 | − | 0.633932i | \(-0.781440\pi\) | ||||
−0.773389 | + | 0.633932i | \(0.781440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | + | 1.73205i | −0.0949158 | + | 0.164399i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.00000 | −0.0940721 | −0.0470360 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470360 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.0000 | 2.23801 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | + | 3.46410i | −0.184900 | + | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.50000 | + | 7.79423i | 0.405751 | + | 0.702782i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.0000 | 2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.00000 | + | 5.19615i | 0.266207 | + | 0.461084i | 0.967879 | − | 0.251416i | \(-0.0808962\pi\) |
−0.701672 | + | 0.712500i | \(0.747563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00000 | + | 3.46410i | 0.176090 | + | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.50000 | + | 12.9904i | −0.655278 | + | 1.13497i | 0.326546 | + | 0.945181i | \(0.394115\pi\) |
−0.981824 | + | 0.189794i | \(0.939218\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.0000 | + | 17.3205i | −0.860663 | + | 1.49071i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.50000 | − | 11.2583i | −0.551323 | − | 0.954919i | −0.998179 | − | 0.0603135i | \(-0.980790\pi\) |
0.446857 | − | 0.894606i | \(-0.352543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.00000 | − | 5.19615i | −0.250873 | − | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | 1.32873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.50000 | + | 6.06218i | −0.288675 | + | 0.500000i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.00000 | + | 8.66025i | −0.409616 | + | 0.709476i | −0.994847 | − | 0.101391i | \(-0.967671\pi\) |
0.585231 | + | 0.810867i | \(0.301004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.0000 | − | 34.6410i | 1.60644 | − | 2.78243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.00000 | − | 6.92820i | 0.319235 | − | 0.552931i | −0.661094 | − | 0.750303i | \(-0.729907\pi\) |
0.980329 | + | 0.197372i | \(0.0632408\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | − | 10.3923i | −0.467099 | − | 0.809040i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | − | 13.8564i | −0.619059 | − | 1.07224i | −0.989658 | − | 0.143448i | \(-0.954181\pi\) |
0.370599 | − | 0.928793i | \(-0.379152\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.00000 | − | 5.19615i | 0.535303 | − | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0000 | + | 22.5167i | −0.988372 | + | 1.71191i | −0.362500 | + | 0.931984i | \(0.618077\pi\) |
−0.625871 | + | 0.779926i | \(0.715256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.500000 | + | 0.866025i | 0.0375823 | + | 0.0650945i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | + | 12.1244i | 0.520306 | + | 0.901196i | 0.999721 | + | 0.0236082i | \(0.00751541\pi\) |
−0.479415 | + | 0.877588i | \(0.659151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | −0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | − | 6.92820i | 0.294086 | − | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | − | 5.19615i | 0.219382 | − | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.00000 | − | 5.19615i | 0.215945 | − | 0.374027i | −0.737620 | − | 0.675216i | \(-0.764050\pi\) |
0.953564 | + | 0.301189i | \(0.0973836\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.00000 | + | 6.92820i | −0.286446 | + | 0.496139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.00000 | + | 15.5885i | 0.637993 | + | 1.10504i | 0.985873 | + | 0.167497i | \(0.0535685\pi\) |
−0.347879 | + | 0.937539i | \(0.613098\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.00000 | 0.634811 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0000 | − | 31.1769i | −1.25717 | − | 2.17749i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | − | 10.3923i | 0.417029 | − | 0.722315i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.50000 | + | 12.9904i | 0.103757 | + | 0.898563i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.00000 | + | 10.3923i | −0.413057 | + | 0.715436i | −0.995222 | − | 0.0976347i | \(-0.968872\pi\) |
0.582165 | + | 0.813070i | \(0.302206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | − | 5.19615i | −0.205557 | − | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.00000 | − | 13.8564i | −0.545595 | − | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.50000 | − | 7.79423i | −0.304082 | − | 0.526685i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.00000 | + | 8.66025i | −0.334825 | + | 0.579934i | −0.983451 | − | 0.181173i | \(-0.942010\pi\) |
0.648626 | + | 0.761107i | \(0.275344\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.0000 | − | 19.0526i | 0.733333 | − | 1.27017i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.0000 | −1.26107 | −0.630537 | − | 0.776159i | \(-0.717165\pi\) | ||||
−0.630537 | + | 0.776159i | \(0.717165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | 0.528655 | 0.264327 | − | 0.964433i | \(-0.414850\pi\) | ||||
0.264327 | + | 0.964433i | \(0.414850\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.50000 | + | 9.52628i | −0.360317 | + | 0.624087i | −0.988013 | − | 0.154371i | \(-0.950665\pi\) |
0.627696 | + | 0.778459i | \(0.283998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −48.0000 | −3.13117 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.00000 | − | 3.46410i | −0.129914 | − | 0.225018i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5000 | − | 18.1865i | −0.676364 | − | 1.17150i | −0.976068 | − | 0.217465i | \(-0.930221\pi\) |
0.299704 | − | 0.954032i | \(-0.403112\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.0000 | − | 24.2487i | 0.894427 | − | 1.54919i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.00000 | − | 5.19615i | 0.445399 | − | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.50000 | − | 4.33013i | 0.158431 | − | 0.274411i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.50000 | + | 4.33013i | 0.157799 | + | 0.273315i | 0.934075 | − | 0.357078i | \(-0.116227\pi\) |
−0.776276 | + | 0.630393i | \(0.782894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | + | 15.5885i | 0.565825 | + | 0.980038i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.50000 | − | 2.59808i | −0.0935674 | − | 0.162064i | 0.815442 | − | 0.578838i | \(-0.196494\pi\) |
−0.909010 | + | 0.416775i | \(0.863160\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | − | 6.92820i | 0.247594 | − | 0.428845i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.00000 | + | 13.8564i | −0.493301 | + | 0.854423i | −0.999970 | − | 0.00771799i | \(-0.997543\pi\) |
0.506669 | + | 0.862141i | \(0.330877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.00000 | − | 3.46410i | 0.121942 | − | 0.211210i | −0.798591 | − | 0.601874i | \(-0.794421\pi\) |
0.920534 | + | 0.390664i | \(0.127754\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000 | − | 17.3205i | 0.607457 | − | 1.05215i | −0.384201 | − | 0.923249i | \(-0.625523\pi\) |
0.991658 | − | 0.128897i | \(-0.0411435\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.5000 | + | 28.5788i | 0.994987 | + | 1.72337i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.0000 | −0.721010 | −0.360505 | − | 0.932757i | \(-0.617396\pi\) | ||||
−0.360505 | + | 0.932757i | \(0.617396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.0000 | − | 17.3205i | −0.598684 | − | 1.03695i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.50000 | + | 11.2583i | 0.387757 | + | 0.671616i | 0.992148 | − | 0.125073i | \(-0.0399165\pi\) |
−0.604390 | + | 0.796689i | \(0.706583\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.50000 | − | 11.2583i | 0.386385 | − | 0.669238i | −0.605575 | − | 0.795788i | \(-0.707057\pi\) |
0.991960 | + | 0.126550i | \(0.0403903\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.0000 | − | 10.3923i | 0.829288 | − | 0.615587i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.500000 | + | 0.866025i | 0.0293105 | + | 0.0507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | − | 3.46410i | −0.116445 | − | 0.201688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.0000 | −0.870388 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | − | 10.3923i | 0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | 0.689382 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.0000 | 1.83231 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.5000 | − | 21.6506i | 0.713413 | − | 1.23567i | −0.250156 | − | 0.968206i | \(-0.580482\pi\) |
0.963569 | − | 0.267461i | \(-0.0861848\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00000 | + | 12.1244i | −0.398216 | + | 0.689730i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.00000 | −0.113410 | −0.0567048 | − | 0.998391i | \(-0.518059\pi\) | ||||
−0.0567048 | + | 0.998391i | \(0.518059\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.50000 | + | 16.4545i | 0.536972 | + | 0.930062i | 0.999065 | + | 0.0432311i | \(0.0137652\pi\) |
−0.462093 | + | 0.886831i | \(0.652902\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | + | 5.19615i | 0.168497 | + | 0.291845i | 0.937892 | − | 0.346929i | \(-0.112775\pi\) |
−0.769395 | + | 0.638774i | \(0.779442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | + | 10.3923i | 0.335936 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.00000 | + | 13.8564i | −0.446516 | + | 0.773389i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | + | 3.46410i | 0.445132 | + | 0.192748i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.0000 | − | 19.0526i | 0.610170 | − | 1.05685i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | −0.714545 | −0.357272 | − | 0.934000i | \(-0.616293\pi\) | ||||
−0.357272 | + | 0.934000i | \(0.616293\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | − | 3.46410i | −0.109599 | − | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −36.0000 | −1.96689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.50000 | + | 2.59808i | −0.0817102 | + | 0.141526i | −0.903985 | − | 0.427565i | \(-0.859372\pi\) |
0.822274 | + | 0.569091i | \(0.192705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.500000 | + | 0.866025i | −0.0271563 | + | 0.0470360i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.0000 | 1.62459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | − | 20.7846i | 0.646058 | − | 1.11901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.50000 | + | 7.79423i | −0.241573 | + | 0.418416i | −0.961162 | − | 0.275983i | \(-0.910997\pi\) |
0.719590 | + | 0.694399i | \(0.244330\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0000 | 1.49881 | 0.749403 | − | 0.662114i | \(-0.230341\pi\) | ||||
0.749403 | + | 0.662114i | \(0.230341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | + | 8.66025i | 0.266880 | + | 0.462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.0000 | 0.585471 | 0.292735 | − | 0.956193i | \(-0.405434\pi\) | ||||
0.292735 | + | 0.956193i | \(0.405434\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000 | + | 20.7846i | 0.636894 | + | 1.10313i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.00000 | − | 1.73205i | 0.0527780 | − | 0.0914141i | −0.838429 | − | 0.545010i | \(-0.816526\pi\) |
0.891207 | + | 0.453596i | \(0.149859\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | + | 4.33013i | −0.973684 | + | 0.227901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | + | 1.73205i | −0.0524864 | + | 0.0909091i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.0000 | + | 31.1769i | 0.942163 | + | 1.63187i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.0000 | + | 22.5167i | 0.678594 | + | 1.17536i | 0.975404 | + | 0.220423i | \(0.0707439\pi\) |
−0.296810 | + | 0.954937i | \(0.595923\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.0000 | −0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.00000 | −0.207112 | −0.103556 | − | 0.994624i | \(-0.533022\pi\) | ||||
−0.103556 | + | 0.994624i | \(0.533022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0000 | − | 20.7846i | 0.619677 | − | 1.07331i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | − | 6.92820i | 0.206010 | − | 0.356821i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | 0.616399 | 0.308199 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.00000 | 0.307389 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.00000 | − | 6.92820i | 0.204390 | − | 0.354015i | −0.745548 | − | 0.666452i | \(-0.767812\pi\) |
0.949938 | + | 0.312437i | \(0.101145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.00000 | + | 3.46410i | 0.101404 | + | 0.175637i | 0.912263 | − | 0.409604i | \(-0.134333\pi\) |
−0.810859 | + | 0.585241i | \(0.801000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.50000 | + | 12.9904i | 0.378325 | + | 0.655278i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | + | 13.8564i | 0.402524 | + | 0.697191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.00000 | + | 12.1244i | −0.351320 | + | 0.608504i | −0.986481 | − | 0.163876i | \(-0.947600\pi\) |
0.635161 | + | 0.772380i | \(0.280934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | − | 2.59808i | 0.0749064 | − | 0.129742i | −0.826139 | − | 0.563466i | \(-0.809468\pi\) |
0.901046 | + | 0.433724i | \(0.142801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0000 | − | 17.3205i | −0.498135 | − | 0.862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.00000 | − | 3.46410i | −0.0993808 | − | 0.172133i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5000 | + | 30.3109i | 0.865319 | + | 1.49878i | 0.866730 | + | 0.498778i | \(0.166218\pi\) |
−0.00141047 | + | 0.999999i | \(0.500449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | −0.443937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0000 | + | 17.3205i | −0.490881 | + | 0.850230i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.0000 | −0.636613 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | + | 19.0526i | −0.536107 | + | 0.928565i | 0.463002 | + | 0.886357i | \(0.346772\pi\) |
−0.999109 | + | 0.0422075i | \(0.986561\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.0000 | + | 20.7846i | −0.583460 | + | 1.01058i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.0000 | 1.06716 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.00000 | −0.289683 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | + | 25.9808i | 0.722525 | + | 1.25145i | 0.959985 | + | 0.280052i | \(0.0903517\pi\) |
−0.237460 | + | 0.971397i | \(0.576315\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00000 | − | 8.66025i | −0.240285 | − | 0.416185i | 0.720511 | − | 0.693444i | \(-0.243907\pi\) |
−0.960795 | + | 0.277259i | \(0.910574\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.00000 | − | 13.8564i | 0.383571 | − | 0.664364i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.0000 | + | 15.5885i | −1.00457 | + | 0.745697i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.00000 | − | 12.1244i | 0.334092 | − | 0.578664i | −0.649218 | − | 0.760602i | \(-0.724904\pi\) |
0.983310 | + | 0.181938i | \(0.0582371\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | − | 12.1244i | −0.333333 | − | 0.577350i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.500000 | + | 0.866025i | 0.0237557 | + | 0.0411461i | 0.877659 | − | 0.479286i | \(-0.159104\pi\) |
−0.853903 | + | 0.520432i | \(0.825771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −72.0000 | −3.41313 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.00000 | + | 8.66025i | 0.236492 | + | 0.409616i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.0000 | 1.55737 | 0.778683 | − | 0.627417i | \(-0.215888\pi\) | ||||
0.778683 | + | 0.627417i | \(0.215888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.5000 | − | 23.3827i | 0.635690 | − | 1.10105i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.00000 | − | 1.73205i | 0.0469841 | − | 0.0813788i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.00000 | + | 8.66025i | −0.233380 | + | 0.404226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.00000 | − | 5.19615i | 0.139724 | − | 0.242009i | −0.787668 | − | 0.616100i | \(-0.788712\pi\) |
0.927392 | + | 0.374091i | \(0.122045\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.0000 | −1.58011 | −0.790057 | − | 0.613033i | \(-0.789949\pi\) | ||||
−0.790057 | + | 0.613033i | \(0.789949\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.0000 | − | 34.6410i | −0.927478 | − | 1.60644i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.00000 | −0.231372 | −0.115686 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115686 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.00000 | − | 6.92820i | −0.184310 | − | 0.319235i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | − | 10.3923i | 0.275880 | − | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.5000 | + | 28.5788i | −1.76650 | + | 1.31129i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | − | 3.46410i | 0.0915737 | − | 0.158610i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0000 | − | 17.3205i | −0.456912 | − | 0.791394i | 0.541884 | − | 0.840453i | \(-0.317711\pi\) |
−0.998796 | + | 0.0490589i | \(0.984378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | − | 3.46410i | −0.0911922 | − | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | − | 3.46410i | −0.0908153 | − | 0.157297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.0000 | −1.17817 | −0.589086 | − | 0.808070i | \(-0.700512\pi\) | ||||
−0.589086 | + | 0.808070i | \(0.700512\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.50000 | − | 9.52628i | 0.248719 | − | 0.430793i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.00000 | − | 13.8564i | 0.361035 | − | 0.625331i | −0.627096 | − | 0.778942i | \(-0.715757\pi\) |
0.988131 | + | 0.153611i | \(0.0490902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00000 | 0.360302 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 24.0000 | 1.07872 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.50000 | − | 6.06218i | 0.156682 | − | 0.271380i | −0.776989 | − | 0.629515i | \(-0.783254\pi\) |
0.933670 | + | 0.358134i | \(0.116587\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.0000 | −0.714827 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.00000 | + | 5.19615i | 0.133763 | + | 0.231685i | 0.925124 | − | 0.379664i | \(-0.123960\pi\) |
−0.791361 | + | 0.611349i | \(0.790627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −48.0000 | −2.13597 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.50000 | − | 7.79423i | −0.199852 | − | 0.346154i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.00000 | + | 13.8564i | 0.354594 | + | 0.614174i | 0.987048 | − | 0.160423i | \(-0.0512858\pi\) |
−0.632455 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.50000 | − | 21.6506i | −0.110378 | − | 0.955899i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.0000 | − | 48.4974i | 1.23383 | − | 2.13705i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.0000 | − | 31.1769i | −0.791639 | − | 1.37116i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.0000 | + | 22.5167i | 0.570637 | + | 0.988372i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.00000 | 0.0438108 | 0.0219054 | − | 0.999760i | \(-0.493027\pi\) | ||||
0.0219054 | + | 0.999760i | \(0.493027\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0000 | + | 17.3205i | 0.437269 | + | 0.757373i | 0.997478 | − | 0.0709788i | \(-0.0226123\pi\) |
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.0000 | − | 17.3205i | 0.435607 | − | 0.754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.00000 | −0.0867926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.0000 | −0.779667 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.0000 | − | 55.4256i | 1.38348 | − | 2.39626i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.50000 | + | 7.79423i | −0.194189 | + | 0.336346i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.0000 | 0.904534 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | + | 3.46410i | 0.0859867 | + | 0.148933i | 0.905811 | − | 0.423681i | \(-0.139262\pi\) |
−0.819825 | + | 0.572615i | \(0.805929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.0000 | 0.600798 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | + | 24.2487i | 0.598597 | + | 1.03680i | 0.993028 | + | 0.117875i | \(0.0376081\pi\) |
−0.394432 | + | 0.918925i | \(0.629059\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.00000 | − | 13.8564i | 0.341432 | − | 0.591377i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.0000 | + | 10.3923i | −0.596420 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.00000 | − | 6.92820i | −0.169791 | − | 0.294086i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.0000 | − | 34.6410i | −0.847427 | − | 1.46779i | −0.883497 | − | 0.468438i | \(-0.844817\pi\) |
0.0360693 | − | 0.999349i | \(-0.488516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.00000 | − | 5.19615i | −0.126660 | − | 0.219382i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.0000 | −0.463595 | −0.231797 | − | 0.972764i | \(-0.574461\pi\) | ||||
−0.231797 | + | 0.972764i | \(0.574461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | − | 3.46410i | 0.0841406 | − | 0.145736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.0000 | −1.92842 | −0.964210 | − | 0.265139i | \(-0.914582\pi\) | ||||
−0.964210 | + | 0.265139i | \(0.914582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.0000 | −0.711428 | −0.355714 | − | 0.934595i | \(-0.615762\pi\) | ||||
−0.355714 | + | 0.934595i | \(0.615762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000 | − | 10.3923i | 0.250654 | − | 0.434145i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.0000 | + | 57.1577i | −1.37620 | + | 2.38364i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.0000 | −1.54033 | −0.770165 | − | 0.637845i | \(-0.779826\pi\) | ||||
−0.770165 | + | 0.637845i | \(0.779826\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.00000 | − | 5.19615i | −0.124676 | − | 0.215945i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.00000 | + | 5.19615i | 0.124247 | + | 0.215203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.00000 | − | 13.8564i | −0.330759 | − | 0.572892i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.00000 | − | 3.46410i | 0.0825488 | − | 0.142979i | −0.821795 | − | 0.569783i | \(-0.807027\pi\) |
0.904344 | + | 0.426804i | \(0.140361\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00000 | + | 43.3013i | 0.206021 | + | 1.78420i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | − | 15.5885i | 0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5000 | + | 18.1865i | 0.431183 | + | 0.746831i | 0.996976 | − | 0.0777165i | \(-0.0247629\pi\) |
−0.565792 | + | 0.824548i | \(0.691430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.0000 | 0.736691 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.0000 | − | 32.9090i | −0.776319 | − | 1.34462i | −0.934050 | − | 0.357142i | \(-0.883751\pi\) |
0.157731 | − | 0.987482i | \(-0.449582\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | −0.530281 | −0.265141 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.00000 | + | 15.5885i | −0.366508 | + | 0.634811i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.00000 | − | 6.92820i | 0.162623 | − | 0.281672i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | + | 20.7846i | −0.485468 | + | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0000 | + | 19.0526i | −0.444286 | + | 0.769526i | −0.998002 | − | 0.0631797i | \(-0.979876\pi\) |
0.553716 | + | 0.832705i | \(0.313209\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.0000 | −1.45166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.50000 | − | 2.59808i | −0.0603877 | − | 0.104595i | 0.834251 | − | 0.551385i | \(-0.185900\pi\) |
−0.894639 | + | 0.446790i | \(0.852567\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0000 | 0.803868 | 0.401934 | − | 0.915669i | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.0000 | − | 25.9808i | −0.601929 | − | 1.04257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5000 | + | 35.5070i | −0.820000 | + | 1.42028i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.0000 | + | 5.19615i | 0.479234 | + | 0.207514i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.00000 | − | 3.46410i | 0.0797452 | − | 0.138123i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000 | + | 6.92820i | 0.159237 | + | 0.275807i | 0.934594 | − | 0.355716i | \(-0.115763\pi\) |
−0.775356 | + | 0.631524i | \(0.782430\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.00000 | + | 10.3923i | 0.238479 | + | 0.413057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.0000 | −0.952411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.00000 | − | 12.1244i | −0.277350 | − | 0.480384i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.5000 | + | 28.5788i | −0.651711 | + | 1.12880i | 0.330997 | + | 0.943632i | \(0.392615\pi\) |
−0.982708 | + | 0.185164i | \(0.940718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.50000 | − | 4.33013i | 0.0985904 | − | 0.170764i | −0.812511 | − | 0.582946i | \(-0.801900\pi\) |
0.911101 | + | 0.412182i | \(0.135233\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.0000 | −0.629999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.0000 | −0.550397 | −0.275198 | − | 0.961387i | \(-0.588744\pi\) | ||||
−0.275198 | + | 0.961387i | \(0.588744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.50000 | − | 2.59808i | 0.0588802 | − | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.0000 | −1.40879 | −0.704394 | − | 0.709809i | \(-0.748781\pi\) | ||||
−0.704394 | + | 0.709809i | \(0.748781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.0000 | − | 51.9615i | −1.17220 | − | 2.03030i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.0000 | 0.702247 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | + | 10.3923i | 0.233727 | + | 0.404827i | 0.958902 | − | 0.283738i | \(-0.0915745\pi\) |
−0.725175 | + | 0.688565i | \(0.758241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.0000 | + | 17.3205i | 0.388955 | + | 0.673690i | 0.992309 | − | 0.123784i | \(-0.0395028\pi\) |
−0.603354 | + | 0.797473i | \(0.706170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.00000 | + | 3.46410i | −0.0776736 | + | 0.134535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0000 | + | 20.7846i | −0.464642 | + | 0.804783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.00000 | + | 8.66025i | 0.193311 | + | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | + | 20.7846i | 0.463255 | + | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0000 | 1.15642 | 0.578208 | − | 0.815890i | \(-0.303752\pi\) | ||||
0.578208 | + | 0.815890i | \(0.303752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −27.5000 | − | 47.6314i | −1.05848 | − | 1.83333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.00000 | 0.0768662 | 0.0384331 | − | 0.999261i | \(-0.487763\pi\) | ||||
0.0384331 | + | 0.999261i | \(0.487763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.50000 | + | 16.4545i | −0.364041 | + | 0.630537i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.0000 | 1.07139 | 0.535695 | − | 0.844411i | \(-0.320050\pi\) | ||||
0.535695 | + | 0.844411i | \(0.320050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.00000 | − | 6.92820i | 0.152610 | − | 0.264327i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00000 | − | 3.46410i | 0.0761939 | − | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0000 | −1.36950 | −0.684752 | − | 0.728776i | \(-0.740090\pi\) | ||||
−0.684752 | + | 0.728776i | \(0.740090\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 52.0000 | 1.97247 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | − | 15.5885i | −0.340899 | − | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.50000 | + | 9.52628i | 0.208029 | + | 0.360317i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | + | 10.3923i | −0.226617 | + | 0.392512i | −0.956803 | − | 0.290736i | \(-0.906100\pi\) |
0.730186 | + | 0.683248i | \(0.239433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00000 | + | 8.66025i | 0.0377157 | + | 0.326628i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.0000 | + | 41.5692i | −0.903892 | + | 1.56559i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.00000 | + | 15.5885i | 0.338002 | + | 0.585437i | 0.984057 | − | 0.177854i | \(-0.0569156\pi\) |
−0.646055 | + | 0.763291i | \(0.723582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.0000 | + | 51.9615i | 1.12351 | + | 1.94597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | 0.897549 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.00000 | − | 10.3923i | 0.224074 | − | 0.388108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.0000 | − | 29.4449i | 0.633993 | − | 1.09811i | −0.352735 | − | 0.935723i | \(-0.614748\pi\) |
0.986728 | − | 0.162385i | \(-0.0519185\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.0000 | −0.780998 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.0000 | + | 38.1051i | −0.817059 | + | 1.41519i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.00000 | − | 6.92820i | 0.148352 | − | 0.256953i | −0.782267 | − | 0.622944i | \(-0.785937\pi\) |
0.930618 | + | 0.365991i | \(0.119270\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | − | 6.92820i | −0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.0000 | − | 24.2487i | −0.516398 | − | 0.894427i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.5000 | − | 23.3827i | −0.497279 | − | 0.861312i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.50000 | + | 4.33013i | −0.0919640 | + | 0.159286i | −0.908337 | − | 0.418238i | \(-0.862648\pi\) |
0.816373 | + | 0.577524i | \(0.195981\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.00000 | − | 8.66025i | −0.0367359 | − | 0.318142i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | − | 5.19615i | 0.110059 | − | 0.190628i | −0.805735 | − | 0.592277i | \(-0.798229\pi\) |
0.915794 | + | 0.401648i | \(0.131563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.0000 | − | 34.6410i | −0.732743 | − | 1.26915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.00000 | + | 8.66025i | 0.182940 | + | 0.316862i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.0000 | − | 32.9090i | −0.693320 | − | 1.20087i | −0.970744 | − | 0.240118i | \(-0.922814\pi\) |
0.277424 | − | 0.960748i | \(-0.410519\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.00000 | 0.182210 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.00000 | + | 6.92820i | −0.145575 | + | 0.252143i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.00000 | − | 12.1244i | 0.254419 | − | 0.440667i | −0.710318 | − | 0.703881i | \(-0.751449\pi\) |
0.964738 | + | 0.263213i | \(0.0847823\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.0000 | 0.653359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.0000 | 0.616250 | 0.308125 | − | 0.951346i | \(-0.400299\pi\) | ||||
0.308125 | + | 0.951346i | \(0.400299\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.00000 | − | 13.8564i | 0.289241 | − | 0.500979i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.00000 | −0.0722158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.00000 | − | 1.73205i | −0.0360609 | − | 0.0624593i | 0.847432 | − | 0.530904i | \(-0.178148\pi\) |
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.00000 | −0.108042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.0000 | + | 45.0333i | 0.935155 | + | 1.61974i | 0.774357 | + | 0.632749i | \(0.218073\pi\) |
0.160798 | + | 0.986987i | \(0.448593\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.0000 | + | 95.2628i | 1.97566 | + | 3.42194i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.0000 | + | 15.5885i | 1.28983 | + | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | + | 15.5885i | −0.322045 | + | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.0000 | − | 17.3205i | −0.357371 | − | 0.618984i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.0000 | + | 27.7128i | 0.571064 | + | 0.989113i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.0000 | −1.46149 | −0.730746 | − | 0.682649i | \(-0.760828\pi\) | ||||
−0.730746 | + | 0.682649i | \(0.760828\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.00000 | + | 13.8564i | 0.284808 | + | 0.493301i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000 | − | 13.8564i | 0.284088 | − | 0.492055i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.00000 | − | 6.92820i | 0.141865 | − | 0.245718i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0000 | −1.48772 | −0.743858 | − | 0.668338i | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0000 | + | 31.1769i | −0.635999 | + | 1.10158i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.5000 | + | 23.3827i | −0.476405 | + | 0.825157i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.00000 | − | 3.46410i | −0.0704033 | − | 0.121942i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.0000 | 0.738321 | 0.369160 | − | 0.929366i | \(-0.379645\pi\) | ||||
0.369160 | + | 0.929366i | \(0.379645\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.0000 | − | 17.3205i | −0.350715 | − | 0.607457i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.0000 | + | 38.1051i | −0.770626 | + | 1.33476i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | + | 6.92820i | 0.559769 | + | 0.242387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.0000 | − | 32.9090i | −0.663105 | − | 1.14853i | −0.979795 | − | 0.200002i | \(-0.935905\pi\) |
0.316691 | − | 0.948529i | \(-0.397428\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.0000 | + | 22.5167i | 0.453152 | + | 0.784881i | 0.998580 | − | 0.0532760i | \(-0.0169663\pi\) |
−0.545428 | + | 0.838157i | \(0.683633\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 33.0000 | 1.14891 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.5000 | − | 47.6314i | −0.956269 | − | 1.65631i | −0.731438 | − | 0.681908i | \(-0.761150\pi\) |
−0.224831 | − | 0.974398i | \(-0.572183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.0000 | 0.416777 | 0.208389 | − | 0.978046i | \(-0.433178\pi\) | ||||
0.208389 | + | 0.978046i | \(0.433178\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.00000 | + | 10.3923i | −0.208138 | + | 0.360505i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.00000 | − | 12.1244i | 0.242536 | − | 0.420084i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.0000 | 2.21481 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −50.0000 | −1.72825 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | − | 11.2583i | 0.224138 | − | 0.388218i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.0000 | 0.447744 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.0000 | + | 31.1769i | 0.619219 | + | 1.07252i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.50000 | − | 11.2583i | −0.223079 | − | 0.386385i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.0000 | − | 36.3731i | 0.719026 | − | 1.24539i | −0.242360 | − | 0.970186i | \(-0.577921\pi\) |
0.961386 | − | 0.275204i | \(-0.0887453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | + | 34.6410i | 0.136797 | + | 1.18470i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.5000 | − | 30.3109i | 0.597789 | − | 1.03540i | −0.395358 | − | 0.918527i | \(-0.629380\pi\) |
0.993147 | − | 0.116873i | \(-0.0372871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.5000 | + | 25.1147i | 0.494734 | + | 0.856904i | 0.999982 | − | 0.00607046i | \(-0.00193230\pi\) |
−0.505248 | + | 0.862974i | \(0.668599\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000 | 0.204242 | 0.102121 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102121 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.0000 | − | 90.0666i | −1.76805 | − | 3.06236i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.00000 | + | 10.3923i | −0.203536 | + | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.00000 | + | 15.5885i | −0.304953 | + | 0.528195i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.00000 | −0.0676897 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0000 | − | 34.6410i | 0.675352 | − | 1.16974i | −0.301014 | − | 0.953620i | \(-0.597325\pi\) |
0.976366 | − | 0.216124i | \(-0.0693416\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.00000 | − | 3.46410i | 0.0674583 | − | 0.116841i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.00000 | 0.235836 | 0.117918 | − | 0.993023i | \(-0.462378\pi\) | ||||
0.117918 | + | 0.993023i | \(0.462378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5000 | − | 37.2391i | −0.723533 | − | 1.25320i | −0.959575 | − | 0.281453i | \(-0.909184\pi\) |
0.236043 | − | 0.971743i | \(-0.424150\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.00000 | −0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.0000 | − | 27.7128i | −0.537227 | − | 0.930505i | −0.999052 | − | 0.0435339i | \(-0.986138\pi\) |
0.461825 | − | 0.886971i | \(-0.347195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | − | 2.59808i | 0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.0000 | − | 31.1769i | 1.40548 | − | 1.04330i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | − | 31.1769i | 0.601674 | − | 1.04213i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | − | 10.3923i | −0.200334 | − | 0.346989i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.0000 | + | 34.6410i | 0.667037 | + | 1.15534i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −56.0000 | −1.86150 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.5000 | − | 42.4352i | 0.813509 | − | 1.40904i | −0.0968843 | − | 0.995296i | \(-0.530888\pi\) |
0.910393 | − | 0.413744i | \(-0.135779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.0000 | + | 20.7846i | −0.398015 | + | 0.689382i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.0000 | −0.463841 | −0.231920 | − | 0.972735i | \(-0.574501\pi\) | ||||
−0.231920 | + | 0.972735i | \(0.574501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.0000 | −0.496428 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.0000 | − | 27.7128i | 0.528944 | − | 0.916157i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.5000 | − | 21.6506i | −0.411889 | − | 0.713413i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.0000 | + | 19.0526i | 0.361678 | + | 0.626444i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.0000 | − | 24.2487i | −0.459820 | − | 0.796432i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.5000 | + | 18.1865i | −0.344494 | + | 0.596681i | −0.985262 | − | 0.171054i | \(-0.945283\pi\) |
0.640768 | + | 0.767735i | \(0.278616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.50000 | + | 30.3109i | 0.114708 | + | 0.993399i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.00000 | + | 1.73205i | −0.0327385 | + | 0.0567048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | + | 20.7846i | 0.392442 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.50000 | − | 9.52628i | −0.179677 | − | 0.311210i | 0.762093 | − | 0.647468i | \(-0.224172\pi\) |
−0.941770 | + | 0.336258i | \(0.890839\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.0000 | 0.620042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.00000 | − | 8.66025i | −0.162995 | − | 0.282316i | 0.772946 | − | 0.634472i | \(-0.218782\pi\) |
−0.935942 | + | 0.352155i | \(0.885449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54.0000 | 1.75848 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.0000 | + | 24.2487i | −0.454939 | + | 0.787977i | −0.998685 | − | 0.0512727i | \(-0.983672\pi\) |
0.543746 | + | 0.839250i | \(0.317006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0000 | 0.584305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000 | 0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.500000 | + | 0.866025i | −0.0161966 | + | 0.0280533i | −0.874010 | − | 0.485908i | \(-0.838489\pi\) |
0.857814 | + | 0.513961i | \(0.171822\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0000 | + | 41.5692i | −0.776622 | + | 1.34515i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.0000 | 0.387905 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.0000 | − | 27.7128i | −0.515593 | − | 0.893033i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.0000 | + | 20.7846i | 0.386294 | + | 0.669080i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.0000 | + | 46.7654i | −0.868261 | + | 1.50387i | −0.00448958 | + | 0.999990i | \(0.501429\pi\) |
−0.863772 | + | 0.503883i | \(0.831904\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.00000 | − | 5.19615i | 0.224872 | − | 0.166924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5000 | − | 45.8993i | 0.850425 | − | 1.47298i | −0.0303994 | − | 0.999538i | \(-0.509678\pi\) |
0.880825 | − | 0.473442i | \(-0.156989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.0000 | − | 19.0526i | −0.352282 | − | 0.610170i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.0000 | −1.50366 | −0.751832 | − | 0.659355i | \(-0.770829\pi\) | ||||
−0.751832 | + | 0.659355i | \(0.770829\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.0000 | − | 46.7654i | −0.862924 | − | 1.49463i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.0000 | + | 27.7128i | −0.510321 | + | 0.883901i | 0.489608 | + | 0.871943i | \(0.337140\pi\) |
−0.999928 | + | 0.0119587i | \(0.996193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | + | 62.3538i | −1.14706 | + | 1.98676i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | + | 6.92820i | −0.127064 | + | 0.220082i | −0.922538 | − | 0.385906i | \(-0.873889\pi\) |
0.795474 | + | 0.605988i | \(0.207222\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.50000 | + | 11.2583i | −0.206271 | + | 0.357272i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −72.0000 | −2.28255 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.0000 | − | 27.7128i | −0.506725 | − | 0.877674i | −0.999970 | − | 0.00778294i | \(-0.997523\pi\) |
0.493245 | − | 0.869891i | \(-0.335811\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.0000 | −0.316386 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1216.2.i.f.961.1 | 2 | ||
4.3 | odd | 2 | 1216.2.i.b.961.1 | 2 | |||
8.3 | odd | 2 | 304.2.i.d.49.1 | 2 | |||
8.5 | even | 2 | 152.2.i.b.49.1 | ✓ | 2 | ||
19.7 | even | 3 | inner | 1216.2.i.f.577.1 | 2 | ||
24.5 | odd | 2 | 1368.2.s.a.505.1 | 2 | |||
24.11 | even | 2 | 2736.2.s.a.1873.1 | 2 | |||
76.7 | odd | 6 | 1216.2.i.b.577.1 | 2 | |||
152.11 | odd | 6 | 5776.2.a.e.1.1 | 1 | |||
152.27 | even | 6 | 5776.2.a.j.1.1 | 1 | |||
152.45 | even | 6 | 152.2.i.b.121.1 | yes | 2 | ||
152.83 | odd | 6 | 304.2.i.d.273.1 | 2 | |||
152.125 | even | 6 | 2888.2.a.d.1.1 | 1 | |||
152.141 | odd | 6 | 2888.2.a.a.1.1 | 1 | |||
456.83 | even | 6 | 2736.2.s.a.577.1 | 2 | |||
456.197 | odd | 6 | 1368.2.s.a.577.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.i.b.49.1 | ✓ | 2 | 8.5 | even | 2 | ||
152.2.i.b.121.1 | yes | 2 | 152.45 | even | 6 | ||
304.2.i.d.49.1 | 2 | 8.3 | odd | 2 | |||
304.2.i.d.273.1 | 2 | 152.83 | odd | 6 | |||
1216.2.i.b.577.1 | 2 | 76.7 | odd | 6 | |||
1216.2.i.b.961.1 | 2 | 4.3 | odd | 2 | |||
1216.2.i.f.577.1 | 2 | 19.7 | even | 3 | inner | ||
1216.2.i.f.961.1 | 2 | 1.1 | even | 1 | trivial | ||
1368.2.s.a.505.1 | 2 | 24.5 | odd | 2 | |||
1368.2.s.a.577.1 | 2 | 456.197 | odd | 6 | |||
2736.2.s.a.577.1 | 2 | 456.83 | even | 6 | |||
2736.2.s.a.1873.1 | 2 | 24.11 | even | 2 | |||
2888.2.a.a.1.1 | 1 | 152.141 | odd | 6 | |||
2888.2.a.d.1.1 | 1 | 152.125 | even | 6 | |||
5776.2.a.e.1.1 | 1 | 152.11 | odd | 6 | |||
5776.2.a.j.1.1 | 1 | 152.27 | even | 6 |